arXiv subjects

Long Huang

Publications and source records attributed to Long Huang.

At least 37 records · Page 2Linked to original sources

arXiv2024

Only the Curve Shape Matters: Training Foundation Models for Zero-Shot Multivariate Time Series Forecasting through Next Curve Shape Prediction

We present General Time Transformer (GTT), an encoder-only style foundation model for zero-shot multivariate time series forecasting. GTT is pretrained on a large dataset of 200M high-quality time series samples spanning diverse domains. In our proposed framework, the task of multivariate time series forecasting is formulated as a channel-wise next curve shape prediction problem, where each time series sample is represented as a sequence of non-overlapping curve shapes with a unified numerical magnitude. GTT is trained to predict the next curve shape based on a window of past curve shapes in a channel-wise manner. Experimental results demonstrate that GTT exhibits superior zero-shot multivariate forecasting capabilities on unseen time series datasets, even surpassing state-of-the-art supervised baselines. Additionally, we investigate the impact of varying GTT model parameters and training dataset scales, observing that the scaling law also holds in the context of zero-shot multivariate time series forecasting.

cs.LG↗

arXiv2024

$L^{\vec{p}}-L^{\vec{q}}$ Boundedness of Multiparameter Forelli-Rudin Type Operators on the Product of Unit Balls of $\mathbb{C}^n$

In this work, we provide a complete characterization of the boundedness of two classes of multiparameter Forelli-Rudin type operators from one mixed-norm Lebesgue space $L^{\vec p}$ to another space $L^{\vec q}$, when $1\leq \vec{p}\leq \vec q<\infty$, equipped with possibly different weights. Using these characterizations, we establish the necessary and sufficient conditions for both $L^{\vec p}-L^{\vec q}$ boundedness of the weighted multiparameter Berezin transform and $L^{\vec p}-A^{\vec q}$ boundedness of the weighted multiparameter Bergman projection, where $A^{\vec q}$ denotes the mixed-norm Bergman space. Our approach presents several novelties. Firstly, we conduct refined integral estimates of holomorphic functions on the unit ball in $\mathbb{C}^n$. Secondly, we adapt the classical Schur's test to different weighted mixed-norm Lebesgue spaces. These improvements are crucial in our proofs and allow us to establish the desired characterization and sharp conditions.

math.CV↗

arXiv2023

Observational constraint on Dark Energy from Quantum Uncertainty

We explore the theoretical possibility that dark energy density is derived from the vacuum particle pairs together with the quantum fluctuation of space-time. By assuming the vacuum particle pairs fall into the horizon boundary of the cosmos with the expansion of the universe, we can deduce the uncertainty in the relative position of particle pairs based on the quantum fluctuation of space-time, which can be used to estimate their or dark energy density. Furthermore, we attempt to explain the origin of negative pressure from the increasing entropy density of the Boltzmann system and derive the equation for the state parameter, which is consistent with the specific equations of state for dark energy. Finally, we fit the models to the SNIa Pantheon sample and Planck 2018 CMB angular power spectra and give statistical results for the cosmology parameters.

gr-qc↗

arXiv2023

The reconstruction of dark energy with Ridge Regression Approach

It may be determined by non-parametric method if the dark energy evolves with time. We propose a method of combining PCA and biased estimation on the basis of ridge regression analysis to reconstruct parameters, meanwhile we present an interesting principal component selection criterion to avoid the arbitrariness of principal component selections, and use numerical integral by Lagrange interpolation to linearize the luminosity distance integral formula in nearly flat space to avoid instability of derivative for functional data. We get the preliminary test results that shows if $Δ\overline w (z) = \overline {\left| {1 + w(z)} \right|} <=0.05$ included $w(z) = -1$, the probability of making a type I error for ${w_{recon}} \ne -1$ is almost zero ($1\% $) in the test; otherwise, if $Δ\overline w (z) = \overline {\left| {1 + w(z)} \right|} > 0.05$, the probability of making a type I error for ${w_{recon}} = -1$ is not more than $10\% $. Finally, we use JLA sample to reconstruct $w(z)$, and the results reject ${\rm{w(z) }} \ne {\rm{ - 1}}$, which is agreement with $ΛCDM$ model.

astro-ph.CO↗

arXiv2022

Model Pruning Based on Quantified Similarity of Feature Maps

Convolutional Neural Networks (CNNs) has been applied in numerous Internet of Things (IoT) devices for multifarious downstream tasks. However, with the increasing amount of data on edge devices, CNNs can hardly complete some tasks in time with limited computing and storage resources. Recently, filter pruning has been regarded as an effective technique to compress and accelerate CNNs, but existing methods rarely prune CNNs from the perspective of compressing high-dimensional tensors. In this paper, we propose a novel theory to find redundant information in three-dimensional tensors, namely Quantified Similarity between Feature Maps (QSFM), and utilize this theory to guide the filter pruning procedure. We perform QSFM on datasets (CIFAR-10, CIFAR-100 and ILSVRC-12) and edge devices, demonstrate that the proposed method can find the redundant information in the neural networks effectively with comparable compression and tolerable drop of accuracy. Without any fine-tuning operation, QSFM can compress ResNet-56 on CIFAR-10 significantly (48.7% FLOPs and 57.9% parameters are reduced) with only a loss of 0.54% in the top-1 accuracy. For the practical application of edge devices, QSFM can accelerate MobileNet-V2 inference speed by 1.53 times with only a loss of 1.23% in the ILSVRC-12 top-1 accuracy.

cs.CV↗

arXiv2022

Real-Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko

This book is devoted to exploring properties of generalized Herz spaces and establishing a complete real-variable theory of Hardy spaces associated with local and global generalized Herz spaces via a totally fresh perspective which means that the authors view these generalized Herz spaces as special cases of ball quasi-Banach function spaces. To be precise, in this book, the authors first study some basic properties of generalized Herz spaces and obtain boundedness and compactness characterizations of commutators on them. Then the authors introduce the associated Herz-Hardy spaces, local Herz-Hardy spaces, and weak Herz-Hardy spaces, and develop a complete real-variable theory of these Herz-Hardy spaces, including their various maximal function, atomic, finite atomic, molecular as well as various Littlewood-Paley function characterizations. As applications, the authors establish the boundedness of some important operators arising from harmonic analysis on these Herz-Hardy spaces. Finally, the inhomogeneous Herz-Hardy spaces and their complete real-variable theory are also investigated. Due to the deficiency of the associate space of the global Herz space, the known real-variable characterizations about Hardy-type spaces associated with ball quasi-Banach function spaces are not applicable to Hardy spaces associated with global generalized Herz spaces which need an improved generalization of the existing one, done by the authors also in this book and having more additional anticipating applications. The authors should also point out that, with the fresh perspective and the improved conclusions on the real-variable theory of Hardy spaces associated with ball quasi-Banach function spaces, the exponents in all the obtained results of this book are sharp. Moreover, all of these results in this book are new and have never been published before.

math.FA↗

arXiv2021

Anisotropic Variable Campanato-Type Spaces and Their Carleson Measure Characterizations

Let $p(\cdot):\ {\mathbb{R}^n}\to(0,\infty)$ be a variable exponent function satisfying the globally log-Hölder continuous condition and $A$ a general expansive matrix on ${\mathbb{R}^n}$. In this article, the authors introduce the anisotropic variable Campanato-type spaces and give some applications. Especially, using the known atom and finite atom characterizations of anisotropic variable Hardy space $H_A^{p(\cdot)}(\mathbb{R}^n)$, the authors prove that this Campanato-type space is the appropriate dual space of $H_A^{p(\cdot)} (\mathbb{R}^n)$ with full range $p(\cdot)$. As applications, the authors first deduce several equivalent characterizations of these Campanato-type spaces. Furthermore, the authors also introduce the anisotropic variable tent spaces and show their atomic decomposition. Combining this and the obtained dual theorem, the Carleson measure characterizations of these anisotropic variable Campanato-type spaces are established.

math.FA↗

arXiv2021

New construction of nine-qubit error-correcting code

We report new construction of nine-qubit error-correcting code, which introduces two new nine-qubit codes and one new three-qubit code. Because both the new two nine-qubit codes have the normal logical operators, as opposed to the nine-qubit Shor code, it results in different performance when the three codes are applied in concatenated quantum error-correction. On the other hand, one of the two nine-qubit codes has the same stabilizer generators as the nine-qubit Shor code, they are more suitable for the high-wight bit-flip noise, and the other code has the different stabilizer generators, which is more suitable for the high-wight phase-flip noise. This work is enlightening to the construction of quantum error-correcting codes, and adds more options for optimizing the performance of quantum error-correction.

quant-ph↗

arXiv2021

Preventing Handheld Phone Distraction for Drivers by Sensing the Gripping Hand

Handheld phone distraction is the leading cause of traffic accidents. However, few efforts have been devoted to detecting when the phone distraction happens, which is a critical input for taking immediate safety measures. This work proposes a phone-use monitoring system, which detects the start of the driver's handheld phone use and eliminates the distraction at once. Specifically, the proposed system emits periodic ultrasonic pulses to sense if the phone is being held in hand or placed on support surfaces (e.g., seat and cup holder) by capturing the unique signal interference resulted from the contact object's damping, reflection and refraction. We derive the short-time Fourier transform from the microphone data to describe such impacts and develop a CNN-based binary classifier to discriminate the phone use between the handheld and the handsfree status. Additionally, we design an adaptive window-based filter to correct the classification errors and identify each handheld phone distraction instance, including its start, end, and duration. Extensive experiments with fourteen people, three phones and two car models show that our system achieves 99% accuracy of recognizing handheld phone-use instances and 0.76-second median error to estimate the distraction's start time.

cs.HC↗

arXiv2021

Classification and purification for the independent quantum channel through quantum error-correction

The essence of quantum error-correction is to use redundant Hilbert space to identify and correct errors, and the channel fidelity of the quantum channel does not affect which errors can be identified and corrected. Based on this, it is found that quantum error-correction can be used to classify the independent quantum channel into 5 types, and 4 of the 5 types can be purified. It is found in quantum error-correction, the decoherence of quantum state may be related to the degree of identification for the state under quantum noise, and the results of this work confirmed that the degree of purity of quantum channel determines its ability to retain the quantum property of the quantum state, not the fidelity. In this work, the identification of the independent Pauli channels by quantum error-correction is demonstrated.

quant-ph↗

arXiv2021

The Constraint of H0from Galaxy clusters and Hubble parameter data

Using comoving distance $d_c$ and angular diameter distance $d_A$, we recalculate parameters describing kinematical state of the universe, still combining the kinematical model of universe but not relying on dynamical equations for gravity. Comoving distance $d_c$ comes from Hubble data H(z) and is more reliable. Angular diameter distance $d_A$ comes from SZE (Sunyaev-Zel dovich Effect) and X-ray data, and needs calibration. In low redshift case, we use expansion of relation between luminosity distance and redshift about redshift $z$; in high redshift case, we take variable substitution $y=1/(1+z)$, and expand the relation between luminosity distance and redshift about variable $y$ in order to reduce computational errors. Finally we get the more precise value of Hubble parameter $H_0=69.13\pm 0.24{\kern 1pt} km{\kern 1pt} \cdot {s^{ - 1}} \cdot Mp{c^{ - 1}}$, corresponding to 0.4\% uncertainty in $68.3\%$ confidence region, also deceleration factor $q_0=-0.57\pm0.04 $ and acceleration rate $j_0=1.28\pm0.33$, and their statistical values and probability graph. We compare the values of ${H_0}$, ${q_0}$, ${j_0}$ with those obtained from other observation data and model.

astro-ph.CO↗

arXiv2020

Signal-to-Noise Ratio of Microwave Photonic Filter With an Interferometric Structure Based on an Incoherent Broadband Optical Source

A comprehensive investigation of the signal-to-noise ratio (SNR) of the microwave photonic filter (MPF) with an interferometric structure based on an incoherent broadband optical source (IBOS) is presented from the time and frequency domains, respectively. The interferometric structure and the IBOS in the MPF result in a beneficial single-bandpass radiofrequency (RF) response. However, the IBOS adds a relatively large noise to the filtered RF signal. Therefore, the analysis of the SNR is of great importance for the design of this kind of MPFs. Theoretical analysis shows that the SNR is a function of the center frequency of the passband, the modulation index, the chromatic dispersion, and the shape of the IBOS. An experiment is performed to verify the theory, and experimental results agree well with the theoretical calculation.

eess.SP↗

arXiv2020

Unified Performance Analysis of Hybrid FSO/RF System with Diversity Combining

Hybrid free space optical (FSO)/radio frequency (RF) systems have been proved to be reliable links for high-data-rate wireless backhauls. In this paper, we present a unified performance analysis of the hybrid FSO/RF transmission system which transmits the identical data in both links and implements two popular diversity combining schemes, namely, selection combining (SC) and maximal ratio combining (MRC), in the receiver. Specially, for the FSO link, the Gamma-Gamma turbulence with pointing errors under heterodyne detection (HD) and intensity modulation/direction detection (IM/DD) is considered in our analysis while the general \k{appa}-μ shadowed fading which unifies popular RF fading models is employed for the analysis of the RF link. As a result, unified closed-form expressions of outage probabilities and average bit error rates for different modulation schemes are derived. Analytical and Monte Carlo simulation results are provided to characterize the performance of the hybrid FSO/RF link which is compared to the single FSO link and the single RF link. The agreement between the analytical and simulation results confirms the unification of various FSO channels and RF fading scenarios into a single closed-form expression.

eess.SP↗

arXiv2019

Real-Variable Characterizations of New Anisotropic Mixed-Norm Hardy Spaces

Let $\vec{p}\in(0,\infty)^n$ and $A$ be a general expansive matrix on $\mathbb{R}^n$. In this article, via the non-tangential grand maximal function, the authors first introduce the anisotropic mixed-norm Hardy spaces $H_A^{\vec{p}}(\mathbb{R}^n)$ associated with $A$ and then establish their radial or non-tangential maximal function characterizations. Moreover, the authors characterize $H_A^{\vec{p}}(\mathbb{R}^n)$, respectively, by means of atoms, finite atoms, Lusin area functions, Littlewood-Paley $g$-functions or $g_λ^\ast$-functions via first establishing an anisotropic Fefferman-Stein vector-valued inequality on the mixed-norm Lebesgue space $L^{\vec{p}}(\mathbb{R}^n)$. In addition, the authors also obtain the duality between $H_A^{\vec{p}}(\mathbb{R}^n)$ and the anisotropic mixed-norm Campanato spaces. As applications, the authors establish a criterion on the boundedness of sublinear operators from $H_A^{\vec{p}}(\mathbb{R}^n)$ into a quasi-Banach space. Applying this criterion, the authors then obtain the boundedness of anisotropic convolutional $δ$-type and non-convolutional $β$-order Calderón-Zygmund operators from $H_A^{\vec{p}}(\mathbb{R}^n)$ to itself [or to $L^{\vec{p}}(\mathbb{R}^n)$]. As a corollary, the boundedness of anisotropic convolutional $δ$-type Calderón-Zygmund operators on the mixed-norm Lebesgue space $L^{\vec{p}}(\mathbb{R}^n)$ with $\vec{p}\in(1,\infty)^n$ is also presented.

math.CA↗

arXiv2019

Robustness of the concatenated quantum error-correction protocol against noise for channels affected by fluctuation

In quantum error correction, the description of noise channel cannot be completely accurate, and fluctuation always appears in noise channel. It is found that when fluctuation of physical noise channel is considered, the average effective channel is dependent only on the average of physical noise channel, and the average of physical noise channel here plays the role of the independent error model in the previous works. Now, one may conclude that in the independent error model, the results in previous works are also valid for average channel where fluctuation exists. In some typical cases, our numerical simulations in the concatenated QEC protocol with 5-qubit code, 7-qubit Steane code and 9-qubit Shor confirm this conjecture. For 5-qubit code, the effective channels are approximate to depolarizing channel as the concatenated level increases. For Steane code, the effective channels are approximate to one Pauli channel as the concatenated level increases. For Shor code, the effective channels are approximate to one of Pauli-$X$ and Pauli-$Z$ channels in each level, and in next concatenated level, the effective channels are approximate to the other. Meanwhile, for these codes, the numerical results indicate that the degree of approximation increases with the concatenated level increases, and the fluctuation of noise channel decays exponentially as concatenated QEC performed. On the error-correction threshold, attenuation ratio of standard deviation of channel fidelity roughly has a stable value. On the other hand, standard deviations of off-diagonal elements of quantum process matrix (Pauli Form) decay more quickly than standard deviations of diagonal elements.

quant-ph↗

arXiv2019

On Function Spaces with Mixed Norms --- A Survey

The targets of this article are threefold. The first one is to give a survey on the recent developments of function spaces with mixed norms, including mixed Lebesgue spaces, iterated weak Lebesgue spaces, weak mixed-norm Lebesgue spaces and mixed Morrey spaces as well as anisotropic mixed-norm Hardy spaces. The second one is to provide a detailed proof for a useful inequality about mixed Lebesgue norms and the Hardy--Littlewood maximal operator and also to improve some known results on the maximal function characterizations of anisotropic mixed-norm Hardy spaces and the boundedness of Calderón--Zygmund operators from these anisotropic mixed-norm Hardy spaces to themselves or to mixed Lebesgue spaces. The last one is to correct some errors and seal some gaps existing in the known articles.

math.CA↗

arXiv2018

Certifying quantumness with the classical fidelity threshold

For a given ensemble of input and target states, the classical fidelity threshold (CFT) is the maximum valve of the averaged fidelity, and it can be achieved with a measure-and-prepare operation. This quantity can be employed to verify whether the channel is in the quantum domain or not. In a recent work by Chiribella and Xie [Phys. Rev. Lett. {\bf 110}, 213601 (2013)], it was showed that all the information about the input and target states can be equivalently described by an entangled state and an effective entanglement-braking (EB) channel, and the CFTs can be defined with the Choi matrix of the effective EB channel. Following this idea, the protocol proposed by Fuchs and Sasaki [Quantum. Inf. Comput, {\bf 3}, 377 (2003)] are reformulated in terms of the effective EB channel, and ss applications, the deterministic and probabilistic CFTs for qubit states and the coherent states are derived in this paper.

quant-ph↗

arXiv2018

Dual Spaces of Anisotropic Mixed-Norm Hardy Spaces

Let $\vec{a}:=(a_1,\ldots,a_n)\in[1,\infty)^n$, $\vec{p}:=(p_1,\ldots,p_n)\in(0,\infty)^n$ and $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$ be the anisotropic mixed-norm Hardy space associated with $\vec{a}$ defined via the non-tangential grand maximal function. In this article, the authors give the dual space of $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$, which was asked by Cleanthous et al. in [J. Geom. Anal. 27 (2017), 2758-2787]. More precisely, via first introducing the anisotropic mixed-norm Campanato space $\mathcal{L}_{\vec{p},\,q,\,s}^{\vec{a}}(\mathbb{R}^n)$ with $q\in[1,\infty]$ and $s\in\mathbb{Z}_+:=\{0,1,\ldots\}$, and applying the known atomic and finite atomic characterizations of $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$, the authors prove that the dual space of $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$ is the space $\mathcal{L}_{\vec{p},\,r',\,s}^{\vec{a}}(\mathbb{R}^n)$ with $\vec{p}\in(0,1]^n$, $r\in(1,\infty]$, $1/r+1/r'=1$ and $s\in[\lfloor\fracν{a_-}(\frac{1}{p_-}-1) \rfloor,\infty)\cap\mathbb{Z}_+$, where $ν:=a_1+\cdots+a_n$, $a_-:=\min\{a_1,\ldots,a_n\}$, $p_-:=\min\{p_1,\ldots,p_n\}$ and, for any $t\in \mathbb{R}$, $\lfloor t\rfloor$ denotes the largest integer not greater than $t$. This duality result is new even for the isotropic mixed-norm Hardy spaces on $\mathbb{R}^n$.

math.CA↗